System and method of process control, particularly papermaking processes in response to fraction defective measurements

ABSTRACT

Disclosed are a system for and method of controlling processes of paper sheet manufacture. In response to basis weight signals at the process wet and dry ends, as well as a moisture signal from the dry end, a proportionality constant indicative of the sheet fiber fraction at the wet end is computed. The proportionality constant is combined with the wet end basis weight output to indicate fiber content at the dry end and control fiber flowing into the papermaking headbox. Control of fiber flow into the headbox and moisture removed by the drying sections is respectively in response to indications of the amount of fiber and moisture at the dry end being less than defective limits. For moisture, the amount of moisture values above a reject limit for moisture is compared with a set point for the amount of moisture values above the reject limit. For fiber content, the amount of fiber values below a reject limit for fiber is compared with a set point for the amount of fiber values below the reject limit. Any difference between the actual amount and the set point will initiate corrective action. The dryers are controlled by wet end moisture and dry end composite profile moisture. The dryers are controlled so that the inherent lag of steam units therein is compensated by heat supplied by trim dryers, having fast response times. To derive instantaneous values of average wet end basis weight, the wet end gauge is normally single-pointed and only periodically scanned across the sheet.

United States Patent [72] Inventors William L. Adams Dublin; Michael P.Grant, Columbus; Richard W. Hickman, Columbus, all of Ohio [211 App].No. 706,059 [22] Filed Feb. 16, 1968 [45] Patented Nov. 23, 1971 [73]Assignee lndustrialNucleonicsCorporation [54] SYSTEM AND METHOD OFPROCESS CONTROL, PARTICULARLY PAPERMAKING PROCESSES IN RESPONSE TOFRACTION DEFECTIVE MEASUREMENTS l6 Claims,6Drawing Figs.

[52] U.S. 162/198, 162/253, 162/263, 235/151.3, 235/151.35 [51] Int.D211 5/06 [501 Field ofSearch 162/198, 252-254, 258, 263; 73/73-76;34/89, 152; 235/151.13,151.3,151.35

[56] References Cited UNITED STATES PATENTS 2,922,475 1/ 1960 Alexander162/252 3,073,153 l/1963 Petitjean 73/73 3,260,642 7/1966 Canter,.lr.... 162/252 2,897,638 8/1959 Maker 51/165.50 3,151,237 9/1964Hrabak..." 235/15l.13 3,260,838 7/1966 Anderson.... 235/151.13 3,490,6891/1970 I-lart'et al..... 162/252X 3,510,374 5/1970 Walker 162/259 XFOREIGN PATENTS 705,626 3/1965 Canada 162/253 MOlSTUlZE SETPT COMPUTERCOMPUTEQ Primary Examiner-S. Leon Bashore Assistant Examiner-AlfredDAndrea, .lr.

Attorneys-Lowe and King, William 'I. Fryer, III, C. Henry Peterson andJames .I. O'Reilly ABSTRACT: Disclosed are a system for and method ofcontrolling processes of paper sheet manufacture. in response to basisweight signals at the process wet and dry ends, as well as a moisturesignal from the dry end, a proportionality constant indicative of thesheet fiber fraction at the wet end is computed. The proportionalityconstant is combined with the wet end basis weight output to indicatefiber content at the dry end and control fiber flowing into thepapermaking headbox. Control of fiber flow into the headbox and moistureremoved by the drying sections is respectively in response toindications of the amount of fiber and moisture at the dry end beingless than defective limits. For moisture, the amount of moisture valuesabove a reject limit for moisture is compared with a set point for theamount of moisture values above the reject limit. For fiber content, theamount of fiber values below a reject limit for fiber is compared with aset point for the amount of fiber values below the reject limit. Anydifi'erence between the actual amount and the set point will initiatecorrective action. The dryers are controlled by wet end moisture and dryend composite profile moisture. The dryers are controlled so that theinherent lag of steam units therein is compensated by heat supplied bytrim dryers, having fast response times. To derive instantaneous valuesof average wet end basis weight, the wet .end gauge is normallysingle-pointed and only periodically scanned across the sheet.

PQOGRAMMER PQOFl LE LEV ELLJNG COMP.

Mms'rune PROHLE CONTROLLERS FRACTlON DEFECTIVE CQMVUTEK SYSTEM ANDMETHOD OF PROCESS CONTROL, PARTICULARLY PAPERMAKING PROCESSES INRESPONSE TO FRACTION DEFECTIVE MEASUREMENTS The present inventionrelates generally to process control systems and methods and moreparticularly to a process controller responsive to signals indicative ofthe amount by which a product deviates from a limiting value.

Process controllers in the prior art have generally been responsive todeviation of the product manufactured from a set point or target value.In many instances, however, it is a desideratum to maintain a propertyas close as possible to a limiting value. One system for maintaining thevalue of a property being manufactured as close as possible to alimiting value is disclosed in the copending application of Charles T.Fitzgerald, Jr., Ser. No. 680,695, filed Nov. 6, 1967, now US. Pat. No.3,515,860, and having a common assignee with the present invention. Inthe Fitzgerald, Jr., invention, a limit value on the property of theproduct is set and control is established in response to the standarddeviation of the product and the limit. While the Fitzgerald, Jr.,invention is readily adapted to control of many processes, it requiresrelatively complicated apparatus for calculating the statisticalvariance or standard deviation, and for making the special compensatingcalculations required where abnormal distributions are encountered.

In accordance with the present invention, the computation of statisticalstandard deviation is not necessary since a product is controlled inresponse to the percentage or fraction defined by the amount of theproduct outside a limiting value divided by the total amount of theproduct. Such a ratio, fraction or percentage is referred to herein asfraction defective. The amount of fraction defective is compared with adesired fraction-defective target or set point value to derive controlsignals for the process manufacturing the product having the computedproperties.

The invention is particularly adaptable to use in conjunction withpapermaking processes. In particular, signals indicative of the moistureand weight of a finished paper product, derived from gauges at the dryend of the process, are utilized for deriving indications offraction-defective moisture and basis weight. The fraction-defectivemoisture and basis weight signals are compared with targetfraction-defective values to derive error signals utilized inconjunction with other signals for controlling fiber flow and drying.

It is, accordingly, an object of the present invention to provide a newand improved process control system and method responsive to statisticalindications of the amount by which a product deviates from a limitingvalue.

Another object of the present invention is to provide a process controlsystem and method responsive to deviations of the defective portion of aproduct from a tolerable amount by which the product may be defective.

Another object of the present invention is to provide, in a papermakingfacility, a method of and apparatus for controlling moisture and/orfiber flow in response to signals indicative of the amount of materialin which the moisture and fiber in the finished product are defectiverelative to set points for the tolerable defective amount.

The above and still further objects, features and advantages of thepresent invention will become apparent upon consideration of thefollowing detailed description of one specific embodiment thereof,especially when taken in conjunction with the accompanying drawings,wherein:

FIG. 1 is a diagram schematically illustrating a preferred embodiment ofthe present invention, in combination with a papermaking facility;

FIG. 2 is a plot indicating possible statistical distribution of aproduct;

FIG. 3 is a block diagram of one of the measuring circuits employed inthe system of FIG. 1;

F IG. 4 is a circuit diagram of a fraction-defective computer in thesystem of FIG. l;

FlG. 5 is a block diagram of the fiber flow controller in the system ofFIG. 1; and

FIG. 6 is a block diagram of the moisture controller in the system ofFIG. 1.

Reference is now made to FIG. 1 of the drawings wherein there isillustrated a control system in accordance with the present invention,in combination with a papermaking facility. The papermaking facility isof the conventional type, including a source 11 of clear water mixedwith a fiber from source 12 in pipe 13. The fiber-water mixture in pipe13 is fed through valves and controllers, described infra, to pump 14.Pump l4.also receives returned white water and feeds the white water andfiber-water mixture in pipe 13 to headbox 15.

Downstream of headbox 15, that includes the usual slice screws 16, isFourdrinier wire 17. Water in the mixture emerging from the sliceopening of headbox 15 is removed to a certain extent by suction andgravity through Fourdrinier wire 17, the drainage of which comprises thewhite water supply for pump 14. Downstream of Fourdrinier wire 17 arewaterremoving press rollers 18, followed by drying section 19 which iscontrolled by the disclosed system as seen infra.

Dryers 19 are divided into two sections, steam .dryers 21, which areheated in response to steam emerging from supply 22 coupled to thedryers via valve 23 and manifold 24. Steam dryers 21 have a relativelylong response time or time constant, on the order of l to 2 minutes astypical values, whereby l or 2 minutes is required for the temperaturechange of the dryers to reach approximately 63 percent of thetemperature change called for by a controller. Dryer section 19 alsoincludes a relatively high-speed, segmented trim dryer 25. Dryer 25 ispreferably positioned downstream of all of the steam dryers 21 butdiffers from the steam dryer by having a fast response time, on theorder of 5 seconds. Dryer 25 is divided into a plurality of separate,controlled sections across the width of the paper sheet. As is known inthe art, such a segmented trim dryer may comprise a plurality ofseparate electric, gas or segmented air dryers.

The relatively moisture-free paper emerging from dryer section 19 ispolished and smoothed by calender rollers 26. The sheet emerging fromrollers 26 is the finished product that is fed to a takeup roller, notshown.

The disclosed system, in addition to controlling the moisture removed bydryer section 19, enables the fiber weight per unit area of the paper tobe controlled both along the sheet length and across the sheet width. Tocontrol the fiber along the sheet length, the ratio of clear water tofiber, that is consistency, of the mixture fed into headbox 15 may becontrolled with valve 35 in the clear water line. The rate at which thefiber-water mixture is applied to pump 14 and headbox is also controlledby valve 36, placed in series with line 13 upstream of pump 14. Therelative weight per unit area of the paper can be controlled as a crossdirection function by adjusting slice screws 16 relative to each other.In addition to being controlled by valves 35 and 36, slice screws 16 anddrives 19, the paper product can be varied in properties by changing therelative pressure between various sections of rollers 18.

Consideration is now given to apparatus utilized for deriving signalsfor driving the various controllers of fiber flow and drying rate.Determinations of the basis weight, i.e., total sheet weight per unitarea, and percent moisture content of the sheet are derived with gaugescapable of scanning the sheet at two separate locations in the process.Between press rollers 18 and steam dryers 21, at the wet end of theprocess, is positioned basis weight gauge 31; while downstream ofcalender rollers 26, at the dry end of the process, are located basisweight gauge 32 and moisture gauge 33. Basis weight gauges 31 and 32 arepreferably of the nucleonic type, including a penetrating radiationsource and radiation detector, while moisture gauge 33 is preferably ofthe capacitance type. Gauges 32 and 33 are both mounted on the samebracket, whereby the moisture and basis weight signals generated therebyprovide measurements of virtually identical sections of the sheet.

Typically, the sheet being manufactured by the mill illustratedpropagates at a velocity on the order of 700 to 1,000 feet per minute,whereby the transport lag in feeding the mixture from pipe 13 to basisweight gauge 31 is on the order of 15 seconds, while the transport lagbetween gauge 31 and gauge 32 or trim dryer 25 is approximately 1minute.

In operation, gauges 31-33 are scanned across the width of the papersheet to derive profile measurements indicative of wet end basis weight,dry end basis weight and moisture. The wet and dry end gauges areselectively scanned across the sheet width at different times inresponse to an output of programmer 41. Gauges 31-33 are alsoselectively driven to a predetermined point across the width of thesheet to derive single point measurements of moisture and basis weight.

The responses of each of gauges 31-33 are respectively derived frommeasuring circuits 42-44, described infra, and may be considered as twoseparate data sets. While the gauges 31-33 are in a scanning mode,measuring circuits 42-44 generate DC voltages indicative of theinstantaneous values of moisture and basis weight detected by thegauges. After a scan of gauges 31-33 has been completed, each of thecorresponding measuring circuits 42-44 computes the average valve forthe previous scan of the property detected thereby. The average value iscompared with the property value at the single point to establish thedifference between the single point property value and the averageproperty value over the scan. The difference between the single pointand average value of the property is combined with the value of theproperty detected by the gauge during the following single pointinterval. Thereby, relatively accurate indications of the average valueof the property are derived while the gauge is in a single point mode.

Programmer 41 controls gauges 31-33 so that the dry end gauges 32 and 33are scanned approximately 95 percent of the time during system operationwhile gauge 31 is scanned only 10 percent of the time. Typically, 2minutes are required for each scan of gauges 31-33; gauges 32 and 33 arein single point operation for 1 minute out of every minutes; gauge 31 isscanned once during every 20 minutes; and during the first minute gauge31 is being scanned gauges 32 and 33 are in the single point mode. It isto be understood that the times stated may be varied and do not includegauge standardization intervals.

In response to the normal operation conditions of the gauges, dry endgauges 32 and 33 drive circuits 43 and 44 so that the circuit outputsare indicative of relatively long-term, low-frequency data indicative ofthe average properties of the sheet over a number of gauge scans at aplurality of points or the average value of property across the sheetwidth scanned. In contrast, gauge 31 derives data generally indicativeof short-term, high-frequency fluctuations of the sheet.

Scanning of gauges 32 and 33 is periodically terminated and they areactivated to the single point mode to enable a relatively constantcontrol action of the process to be computed for the same cross machineand machine direction region of the sheet as detected by gauge 31 at atime while it was in the single point mode. To this end, gauges 32 and33 are driven by programmer 41 to a predetermined point across the widthof the sheet for approximately 1 minute out of every 20 minutes. Thesingle point position of gauges 32 and 33 is the same distance from thesheet edge as the single point position of gauge 31 and begins 1 minuteafter gauge 31 was removed from the single point condition and beganscanning. Since there is a 1-minute transport lag between wet end gauge31 and dry end gauges 32 and 33, the single pointing dry end gauges areresponsive to about the same portion of the sheet as was detected bygauge 31 during the last minute of its single point operation prior tothe scan. The signals generated by circuits 42-44 for the l minute whiledry end gauges 32 and 33 are in the single point mode can be made tocoincide in time for the same portion of the sheet by delaying the wetend basis weight signal derived from measuring circuit 42. By combiningthe delayed signal from the wet end with signals derived from the dryend during the single point mode, the relatively constant wet end fiberfraction introduced by the Fourdrinier and presses is thereby determinedperiodically. In particular, the wet end fiber fraction, k, isdetermined by computing the sheet fiber content (BDBW), frequentlyreferred to as bone dry basis weight, from single point outputs of dryend gauges 32 and 33, and taking the ratio of the fiber content to theWet end basis weight.

To derive the wet end fiber fraction signal, the wet end basis weight(WEBW) output signal of measuring circuit 42 is applied continuously toDC analog integrating network 46 which drives l-minute delay network 45.Integrating network 46 has a time constant selected whereby the outputvoltage derived thereby is indicative of the signal applied thereto forthe preceding minute. Thereby, for the minute while dry end gauges 32and 33 are in the single point mode, the output of delay unit 45 isindicative of the average wet end basis weight of the portion of thesheet being detected by gauges 32 and 33.

To compute the sheet fiber content at the dry end, the DC analog outputvoltages of measuring circuits 43 and 44 are selectively applied to theinputs of analog multiplier 47 and subtracter 48, respectively. Theoutput signals of circuits 43 and 44 are fed to multiplier 47 andsubtracter 48 through the normally open-circuited contacts of switches51 and 52, which contacts are closed in response to the output ofprogrammer 41 only during the 1 minute while dry end gauges 32 and 33are in single point operation. Subtraction circuit 48 responds to aconstant DC voltage having a value proportional to one, as well as tothe output of moisture-measuring circuit 44. Since the output ofmoisture-measuring circuit 44 is proportional to the prevent moisturecontent of the weight per unit area of the sheet at the dry end of theprocess, subtracter 48 derives a DC voltage indicative of fiberpercentage, by Weight, in the sheet at the dry end. The percent fiberindicating output signal of subtracter 48 is multiplied by the dry endbasis weight signal derived from measuring circuit 43 in multiplier 47,having a DC output voltage proportional to weight per unit area of fiberat the dry end (BDBW), a term frequently referred to in the art as bonedry basis weight.

The bone dry basis weight output voltage of multiplier 47 is applied toDC analog integrator 53, having a time constant equal to 1 minute,whereby the integrator derives a DC output voltage proportional to theaverage bone dry basis weight of the sheet at the dry end for the 1minute while the gauges were activated to the single point mode.Thereby, upon completion of the 1 minute period of gauges 32 and 33activated to the single point mode, the output voltages of delay unit 45and integrator 53 are DC voltages respectively representing the averagewet end weight (WEEW)and average bone dry basis weight (BDBW) foridenticarpbrtions of the sheet. To compute the ziinauirref moistureremoved from the sheet by dryer section 19 while the dry end gauges 32and 33 were in the single point mode, the output voltages of delayelement 45 and integrator 53 are continuously applied as divisor anddividend inputs respectively to analog division circuit 54. Divisioncircuit 54 responds to the two DC analog signals applied thereto toderive a DC analog output voltage indicative of a relatively stableadaptive proportionality constant, k, indicative of the fraction of thebasis weight at the wet end which is made up of fiber. Theproportionality constant is therefore computed as:

w ll? WEBW (1) At the termination of the 1 minute period of gauges 32and 33 being in the single point mode, the output voltage of divider 54is gated through the normally open circuit contacts of switch 55 toanalog memory 56. The contacts of switch 55 are closed for a relativelyshort time interval in response to a control signal from programmer 41as each 1 minute single point mode operation of gauges 32 and 33 isbeing completed to load memory 56 with a new value of k, which isindependent of any prior k value which may have been stored in thememory. Initially, memory 56 is preloaded with a value of k based on apriori knowledge of the paper machine characteristics.

Once a k value is stored in memory 56 it is available to be continuouslyread from the memory into apparatus for computing wet end moisture(M,,,) and predicted bone dry basis weight (13 1.)) in response to basisweight signals derived from wet end basis weight gauge 31. The k valuestored in memory 56 is utilized effectively to enable the fiber contentor bone dry basis weight of the sheet portion passing wet end gauge 31to be derived because the amount of moisture which dryer section 19removes from the sheet remains relatively constant over a 20-minuteperiod between calculations of k. The derivation of fiber contentsignals from the wet end gauge 31 output enables fiber flow control tobe effected after approximately a l5-second transport lag.

The value of k stored in memory 56 is combined with the instantaneouswet end basis weight (WEBW) signal derived from gauge 31 and measuringcircuit 42 to compute predicted dry end bone dry basis weight and wetend moisture weight per unit area as:

BD=(WEBW) k (2), and

M,,.=WEBW (1k) (3). From equations 2 and 3 it is appreciated that thevalue of k is, in efiect, a proportionality constant utilized fordetermining predicted bone dry and wet end moisture weight per unitarea. Since the valve of k is computed in response to actualmeasurements made on the process and is not established on an a prioribasis once the process has been in operation, the system can beconsidered as adaptive and k as an adaptive function.

To determine the values of BD and M,,., the DC output voltage of memory56 is combined with the DC wet end basis weight output voltage ofmeasuring circuit 42 in a computer comprising analog multipliers 57 and58, as well as analog subtraction network 59. Multiplication network 57responds to the output voltages of memory 56 and measuring circuit 42 toderive a DC voltage proportional to the value of predicted bone drybasis weight, as determined by equation 2. The solution of Equation 3involves feeding the output of memory 56 to subtraction network 59, thesubtrahend input of which is a constant DC voltage proportional to one.Thereby, subtraction network 59 derives a DC analog output voltageindicative of the percent moisture in the sheet at the wet end. Thefiber indicating output voltage of subtracter 59 is multiplied by thebasis weight output signal of measuring circuit 42 in multiplyingnetwork 58, having a DC analog output voltage proportional to the totalwet end moisture detected by gauge 31.

The predicted bone dry and wet end moisture signals respectively derivedfrom multipliers 57 and 58 are utilized in a manner described infra forrespectively controlling the flow of fiber into pump 14 and the amountof moisture removed from the sheet by dryer 19. Because sheet fibercontent is calculated in response to measurements made at relativelyearly or upstream portion of the process, fiber flow control can be madecontinuously or on a periodic basis of once every 15 seconds, thetransport lag between the fiber-water inlet to pump 14 and wet end gauge31. In contrast, fiber measurements made exclusively from dry end gauges32 and 33, enable fiber flow adjustments approximately every 1.5minutes. The calculation of wet end moisture enables dryer section 19 tobe controlled to anticipate changes in the moisture of the sheet beingfed to the dryer. Before considering the manner by which the outputsignals of multipliers 57 and 58 control the fiber flow to pump 14 andheadbox 15, as well as the desorption rate of dryers 19, a descriptionwill be given to the method and apparatus for deriving other controlparameters affecting fiber flow and moisture.

In addition to control by the outputs of multipliers 57 and 58, thefiber flowing into pump 14 and the desorbing properties of dryer 19 areresponsive to signals representing amount of unacceptable product in thesheet passing dry end gauges 32 and 33. In the manufacture of paper, asall other products, the finished product has varying qualities which canbe determined on a statistical basis. In paper manufacture, the qualityof the product is determined by, inter alia, the grade of fiberintroduced into the process from source 12, the conditions of headboxl5, Fourdrinier wire 17, and the felts on rollers 18. If the processproduces a product having properties conforming with a normalstatistical distribution, a curve of the values of the property versusthe amount of the product having the stated property values has thefamiliar, bell-shaped normal distribution curve. The maximum point onthe curve is identical with the average value of the product produced.If the process produces a product conforming with the normaldistribution, the process can be controlled in response to a functionrelated to standard deviation. In particular, if a limit is set on theamount a product property may fall outside of a certain standarddeviation, the average value of the product produced by the process canbe controlled. Such a system and method for controlling a process isdisclosed in the copending application of Charles T. Fitzgerald, Jr.,Ser. No. 680,695, filed Nov. 6, 1967, bearing the title ProcessController with Dynamic Set-Point Adjustment Responsive to theStatistical Variance of the Controlled Property, now U.S. Pat. No.3,515,860, and commonly assigned with the present invention. Acontroller of the type disclosed by the Fitzgerald, Jr., applicationcould be utilized in the present combination and connected to beresponsive to the outputs of basis weight and moisture measuringcircuits 43 and 44.

One problem, however, with the system and method disclosed in saidFitzgerald, Jr., application is that the statistical computations becomerather complex when the product does not follow a normal distribution.In paper manufacture, moisture and basis weight value commonly do nothave a normal distribution. In the presently disclosed system, thequality of the paper product is determined by measuring the fraction ofpercentage defective of the sheet having amounts of moisture and basisweight exceeding limits at the process dry end.

To explain the concept of fraction defective, reference is now made toFIG. 2 of the drawings, wherein there is plotted a graph of papermoisture distribution about an average. In particular, the abscissa inFIG. 2 represents moisture content, while the ordinate representsamounts of the sheet having a particular moisture content. Thedistribution of moisture in the product illustrated by FIG. 2 is notnormal, as seen from the clips in the curve; it does follow generalstatistical laws since the ordinate values of the curve approach zero asthe deviation from the mean moisture content, M, approaches infinity.

It can be determined that the product should be rejected or isunacceptable if the moisture thereof is more than a predetermined level,indicated on FIG. 2 by the vertical line labeled Reject Limit. Foreconomy purposes, however, the paper maker is willing to accept theproduct even though it has a moisture content above the reject limit.The ratio of paper having a moisture content more than the reject limitto the total amount of papermoisture content is referred to as fractiondefective and is represented as the ratio of the area below the curveand to the right of the reject limit to the total area below the curve.Stated mathematically, moisture fraction defective, MFD), is expressedas:

MFD: ti+ ldt where:

M is the instantaneous value of moisture detected by dry end gauge 33,

M is the moisture reject limit, indicated on FIG. 2 and preselected bythe paper manufacturer,

[is time,

T is the length of an integration or averaging interval, generally equalto ID minutes,

t, is the instant of time at which the integration interval T begins,

f( MM for M less than M and f( M-M )=l for M equal to or greater than MTo determine fraction defective of moisture in the finished paperproduct at the dry end of the process, the DC output voltage ofmeasuring circuit 44 is continuously applied tofraction-defective-computing network 61, having analog computercircuitry described infra in conjunction with FIG. 4. Fraction-defectivecalculator 61 is also responsive to a DC input voltage, set by anoperator, to represent the desired or set point moisture reject limit.Fraction-defective computer 61 continuously derives a very slowlyvarying DC output voltage in accordance with equation 4 and indicativeof what percentage of the time the paper measured by gauge 33 has amoisture content greater than the limit M Computer 61 is activated inresponse to the output of programmer 41 so that integrators therein arereset to a zero level periodically; a convenient resetting time beingwhile gauges 32 and 33 are in the single point operating mode once every20 minutes.

The output signal of computer 61 is fed to analog subtraction circuit62, having a minuend signal comprised of a DC voltage set by an operatorto equal the percent or fraction defective the paper maker is willing toaccept; typically the value set by the operator is about 3 percent.Thereby subtraction circuit 62 derives continuously a very slowlyvarying DC error signal indicative of the deviation of the actual dryend fraction defective from the set point moisture fraction defective.If the signal from computer 61 is larger than the set point moisturefraction-defective signal, the result of the subtraction is negative,whereby the error signal output from the subtraction circuit will haveone polarity. If the computer 61 output signal is smaller than the setpoint signal, the result of the subtraction is positive,'whereby thesubtraction circuit output will have the opposite polarity.

In accordance with the same theory as was developed for moisturefraction-defective computation, computer 63 responds continuously to theoutput of basis weight and moisturemeasuring circuits 43 and 44 toderive indications of fraction-defective fiber content. One differencebetween computers 61 and 63 is that the former determines fractiondefective in response to moisture values above a reject limit, while thelatter calculates fraction defective in response to fiber contentsignals less than a reject limit. It is also to be noted that forcertain types of paper the calculation of moisture fraction defective isresponsive to variations above and below moisture rejection limits.

The fiber content signal coupled to computer 63 is derived by feedingthe moisture output signal of circuit 44 to the minuend input of analogsubtraction network 78, having a subtrahend input responsive to aconstant DC voltage proportional to unity. The DC difference outputvoltage of subtracter 78, proportional to fiber percentage, is appliedto an input of multiplier 79, the other input of which is the DC dry endbasis weight output voltage of circuit 43. Multiplier 79 generates a DCoutput voltage representing fiber weight of the finished paper productin response to the inputs thereto, which voltage is coupled to fractiondefective computer 63. Computer 63 responds to the actual fiber weightsignal applied thereto by multiplier 79, and an analog DC set pointvoltage indicative of the fiber weight reject limit, (BDBW), acceptableto derive a fraction-defective output signal in the same mannerindicated supra regarding computer 61. The DC output voltage of computer63 is compared in subtracter 64 with a set point indicating DC voltagethat represents the desired value of dry end fiber fraction defective,BDBW Generally, however, a paper maker does not determine the quality ofthe finished product in terms of fiber content, i.e., bone dry basisweight, but determines the product quality as a function of dry endmoisture and basis weight. To compute the bone dry limit, therefore, theoperator feeds into the system voltages from DC sources (not shown)representing dry end basis weight and moisture limits into a fibercontent computer connected in the same manner as subtracter 78 andmultiplier 79. The fraction defective of fiber content is the same asfraction defective for dry end basis weight because fraction defectiveis a ratio of acceptable product to total product and as such is notchanged by equal variations of multiplying terms in the numerator anddenominator. Thereby, the BDBW input signal to subtractor 64 can bemerely relabeled BW basis weight fraction defective desired. The erroris insignificant for normal moisture content.

The error signals generated by subtraction networks 62 and 64 areintegrated by integrators 262 and 264 respectively, and respectivelycombined with the output voltages of multipliers 57 and 58 to controlthe flow of fiber into pump 14 and headbox 15 and the drying rate ofdryer section 19 in a manner tending to reduce the error signals tozero. As long as the computed value of a fraction defective is equal tothe set point for the fraction defective, the error signal remains atzero, and the output of the associated integrator 262 or 264 will remainconstant. However, if the computed fraction defective deviates from theset point value, the error signal will no longer be zero, and theintegrator output will change in a direction dependent on the errorsignal polarity. Since the integrator output provides a baising signal,or effectively a set point signal, to moisture controller 66 or fiberflow computer 82, the change in the integrator output will change theoperating point of the associated moisture or fiber controller in such adirection as to equalize the computed fraction defective with therespective set point value for the fraction defective, thereby reducingthe error signal to zero as aforesaid.

As is explained in the Fitzgerald patent, supra, an automatic controllermaintains the mean value of the process, as shown in FIG. 2 hereof,substantially equal to the controller set point or target value. Sincethe entire process distribution moves to the right or to the left whenthe controller set point is changed, as is shown for example by FIGS. 3and 4 of the Fitzgerald patent, in order to make more rejects (higherfraction defective) the target value is adjusted so as to approach thelimit. Conversely, in order to make fewer rejects (lower fractiondefective) the target value is adjusted so as to recede from the limit,

The manner by which the output signals of multiplier 58 and integrator262 are combined in controller 66 for activating dryer section 19 willnow be considered. Broadly; controller 66 derives a signal representingthe total amount of moisture to be withdrawn from the sheet by thedryier sections 21 and 25 and feeds the sections so that the relativelyslow response time of steam dryers 21 is compensated with segmented trimdryers 25, having a relatively fast speed of response. Because of thel-minute transport lag between wet end gauge 31 and high-speed trimdryer 25, there is a l-minute delay between the time a wet end moisturesignal is derived from gauge 31 and the application of that signal tothe trim dryer. In contrast, the wet end moisture signal derived fromgauge 31 is applied immediately to slow response steam dryers 21. Tomaintain the total drying rate of dryer section 19 at a leveldeten'nined by the output voltages of multiplier 58 and integrator 262and independent of the divergent dryer response times, a feedback loopbetween the dryer sections is provided.

As described in detail infra in conjunction with FIG. 6, controller 66responds to the wet end moisture indicating output of multiplier 58 toderive a signal that is immediately coupled as a DC set point inputvoltage for a servoloop controlling steam dryers 21. The servoloop isalso responsive to a DC voltage proportional to the actual drying rateof steam dryer 21 in response to signals derived from temperaturetransducers 68 and 69, mounted on each of the cylinders comprising thesteam dryer. For purposes of simplicity, only the transducers 68 and 69for two of the steam drying cylinders is illustrated. The signals fromall of the temperature transducers are fed to computer 71, whichgenerates signals representing average temperature for the cylinderscomprising steam dryer 21. The average temperature signal is utilized bycomputer 71 to derive a DC output voltage indicative of actual dryingrate in steam dryer 21. The output of computer 71 is coupled to theservoloop in controller 66 and compared with the steam dryer set inputderived in the controller to drive controller 72 for valve 23 in thesteam supply line. Controller 72 is preferably of the integral typedescribed in Spergel et al., US. Pat. No. 2,955,206.

High-speed, fast-response time trim dryer 25 is driven in response tothe inputs to controller 66 in an entirely different manner from thatutilized for driving steam dryer 21. in particular, controller 66 drivesdryer 25 in response to a signal indicative of the desired drying rateof dryer 19, which signal is generated by combining the slowly varyingmoisture fractiondefective error signal derived from integrator 262 witha delayed replica of the wet end moisture indicating output signal ofmultiplier 58. The wet end moisture signal is delayed by the l-minutetransport lag between gauge 31 and trim dryer 25 because of the trimdryer high speed of response. To compensate for the response timeproperties of steam dryer 21, trim dryer 25 is also driven in responseto the output of computer 71, indicative of the actual drying rate ofsteam dryer 21. The signals indicative of desired total drying rate andthe actual drying rate of dryer 21 are combined in a'second servoloopwith the DC output of temperature transducer 65. Transducer 65 ismounted in trim dryer 25 so that the signal it generates is proportionalto the actual trim dryer drying rate. Thereby, the error signal of thesecond servoloop is a DC signal indicating the drying rate set point fortrim dryer 25 to satisfy the indicated drying rate for the entire dryersection 19. The error signal of the second servoloop is derived bycontroller 66 on lead 70 and is fed in a like manner to each segment oftrim dryer 25 via adding networks 77 and dryer actuators 73, describedinfra. As time progresses and the actual drying rate of steam dryer 21changes to catch up with the variations in detected wet end moisture,the error signal driving actuators 73 decreases, accompanied by a returnof the trim dryer drive signal on lead 70 to approximately the samevalue as prior to a detected moisture change derived form multiplier 58.

According to another feature of the disclosed system, variations of wetend moisture for different points across the width of the sheet, i.e.,at different cross machine direction locations, are compensated byderiving a composite moisture profile in response to the output of dryend scanning moisture gauge 33. The composite moisture profile isrepresentative of the average moisture at different cross machinedirection points over a relatively large number of scans of moisturegauge 33; typically the number of scans is selected as ten. To computesignals indicative of composite moisture profile, the output ofmeasuring circuit 44 is applied to computer 75, which preferably takes aform described and illustrated in the copending application of Edward J.Freeh, Ser. No. 682,336, filed Nov. 13, 1067, and commonly assigned withthe present invention. Composite moisture profile computer 75 isactivated during the 95 percent of the time moisture gauge 33 is in thescanning mode, but is deactivated by programmer 41 while gauge 33 is inthe single point mode. Moisture profile computer 75 is decoupled fromgauge 33 while the gauge is in a single point 'mode because no profiledata are being derived from the gauge at such times. Moisture profilecomputer 75 includes a plurality of outputs, equal in number to thenumber of segments in trim dryer 25, whereby it derives voltagesindicative of the average moisture at a plurality of cross directionregions in response to several gauge scans atdifferent machine directionlocations. The output signals of composite moisture computer 75 areapplied to profile leveling computer 76, having a number of outputsequal to the quantity of trim dryer sections. Computer 76 compares theseparate profile signals to derive control voltages on its output leadswhereby each of the trim dryer sections is adjusted so that the sheethas a consistent moisture across its entire width. Profilelevelingcomputer 76 is described in either of US. Pat. No. 3,040,807 or3,214,845, issued respectively to Chope and Huffman on June 26, 1962,and Nov. 2, 1965.

Each of the outputs of profile-leveling computer 76 is added in a likemanner with the trim dryer output signal of controller 66 in a bank ofadding circuits 77, equal in number to the number of segments of trimdryer 25. The analog output signals from each of the adders in bank 77is applied to a separate one of the controllers in bank 73, whichcontrollers generate power in accordance with the required heat in eachof the sections of trim dryer 25. Thus, trim dryers 25 serve a dualfunction of leveling profile variations in the moisture content of thesheet and compensating for the lag of slowresponse steam dryers 21.

According to another aspect of the present system, the fiber content inthe cross machine direction is adjusted so that it is relativelyconsistent. To this end, a composite fiber profile is derived from dryend gauges 32 and 33 to control the positions of screws 16 comprisingthe slice of headbox 15. The fiber content at the dry end of the processis calculated on an instantaneous basis in response to the outputs ofdry end basis weight-measuring circuit 43 and moisture-measuring circuit44 by subtraction network 78 and multiplier 79, as indicated supra. Theoutput signal of multiplier 79 is fed to composite fiber profilecontroller 81, actuated in response to the output of programmer 41 atall times except when gauges 32 and 33 are in the single point mode.Controller 81 responds to successive scans of gauges 32 and 33 to derivea plurality of output signals, equal in number to the number of slicescrews 16, The output signals of controller 81 are voltages indicatingthe amount by which a particular slice screw 16 must be adjusted toachieve uniformity of fiber content across the width of the sheet. Theapparatus comprising controller 81 is similar to that described suprawith regard to composite moisture profile computer 75 andprofile-leveling computer 76. The several output signals of controller81 are applied to separate motors (not shown) for driving slice screws16.

in addition to the cross direction fiber control performed by controller81 on slice screws 16, the present system provides means for controllingthe fiber flow into headbox 15, whereby the total fiber in the sheet,along its length or in the machine direction, is maintained withinbounds. A set point signal for the amount of fiber flow into pump 14 andheadbox 15 is derived in response to the relatively high frequencypredicted bone dry or fiber content output signal of multiplier 57 andthe slowly varying fiber content error fraction-defective output signalof integrator 264. Because fiber flow control is in response to thefiber content signal derived from measurements made at the wet end ofthe process, at a transport lag position close to the fiber flow inlet,relatively continuous control of fiber fiow can be attained.

The output signals of multiplier 57 and integrator 264 are combined toderive a fiber flow set point in fiber flow computer 82. Fiber flowcomputer 82 derives a fiber flow set point output by subtracting apredetermined DC voltage representing a predetermined value of fibercontent based on a priori knowledge from the predicted fiber contentsignal generated by multiplier 57. The resulting error signal betweenthe predicted and predetermined fiber content is multiplied by aconstant and added with the integrated fiber content fraction-defectiveerror output signal generated by integrator 264. Stated mathematically,the value of output signal, F, derived by computer 82 is expressed as: v

F= Q(BDBDO) +f BDBWFDE dt 6 where: V 7 7 V redicted instantaneous bonedry output of multiplier b =predetermined fiber content,

Q=a constant, and

(BDBWFDE)=the error of fiber content fraction defective.

The fiber flow set point output voltage of computer 82 is integrated byintegrator 282 and fed to fiber flow controller 84, described in detailinfra in conjunction with FIG. 4, which derives output signals tocontrol the amount of fiber flowing into pump 14 from source 12 byadjusting valves 35 and 36.

Fiber flow controller 84 responds to the output of fiber flow computer82 so that with a predetermined setting of water flow valve 35, mixturevalve 36 is adjusted until a maximum flow rate that the system canhandle is attained. After the maximum flow rate that the system canhandle is attained by opening valve 36 to its fullest extent, the ratioof fiber to clear water flowing into pipe 13 is changed from thepreadjusted value by adjusting valve 35 to satisfy the set point outputof fiow computer 82.

Control of valves 35 and 36 in response to the consistency and flowindicating output voltages derived from fiber flow controller 84 is bymeans of conventional servo feedback loops. In particular, theconsistency or percentage fiber of the material flowing in line 13 ismeasured with gauge 85, the output signal of which is a DC voltage thatis compared with the consistency output signal of fiber flow controller84 in subtraction network 86. The error signal derived from subtractionnetwork 86 is fed to servo 87 that adjusts the setting of valve 35. Thevolume flow rate of material moving through the line through valve 36 ismeasured with flow meter 88, deriving a DC output signal which iscompared in subtraction network 89 with the desired or set point forflow through valve 36. The error signal derived from subtraction network89 is fed to servoactuator 91, whereby the set point flow rate output ofcontroller 84 is maintained.

Consideration is now given to the apparatus and operating mode ofmeasuring circuit 42 by referring to FIG. 3. Broadly, measuring circuit42 computes average basis weight for the entire sheet while gauge 31 isin the single point mode by initially calculating the profile averagebasis weight in response to gauge 31 scanning across the sheet width.The computed average basis weight signal is compared with the basisweight at the cross machine direction point where gauge 31 is locatedduring the single point mode, whereby an error between the selectedpoint and average basis weight is established. The error voltage iscombined with the basis weight gauge output signal while the gauge is inthe single point mode to derive the indication of average basis weighton an instantaneous basis,

To these ends, the DC analog voltage generated by basis weight gauge 31is coupled to three parallel channels, respectively includingsubtraction circuit 101, sample-and-hold circuit 102 andprofile-averaging computer 103. Profile-averaging computer 103 isresponsive to signals from programmer 41, whereby the averaging processis preformed only while gauge 31 is being scanned across the width ofthe sheet. In contrast, sample-and-hold network 102 is responsive to theoutput of basis weight gauge 31 whenever the scanning gauge passes overthe preselected point where the gauge is driven while it is in thesingle point mode. The output voltages of sample-and-hold network 102and profile-averaging computer 103 are respectively supplied as minuendand subtrahend input signals to analog computer subtracter 104. Hence,upon the completion of a scan of gauge 31 across the width of the sheet,the output voltage of subtracter 104 is a signal representing thedifference in basis weight at the selected point from the average basisweight across the entire sheet.

The output voltage of difference network 104 is coupled through switch105 to analog memory 106 upon the completion of a scan of gauge 31 inresponse to the switch being closed by the programmer at that time.Analog memory 106 stores the signal fed thereto through switch 105 untilanother signal is fed to the memory in response to the next closure ofthe contacts of switch 105. The output of analog memory 106 iscontinuously derived and normally fed through the contacts of normallyclosed switch 107 to the subtrahend input of difference network 101, theminuend input signal of which is responsive to the output of basisweight gauge 31. Switch 107 is normally maintained in the closedposition in response to signals from programmer 41,,except during theinterval when gauge 31 isbeing scanned across the sheet. Thereby, at alltimes while basis weight gauge 31 is in a single point mode, thedifference output signal of subtracter 101 is a DC analog voltagerepressnting the average basis weight of the sheet as it passes wet endgauge 31.

To determine the average basis weight of the sheet while gauge 31 isscanning across the sheet, the value of the profile average during thepreceding scan of the gauge is stored. The stored voltage is comparedwith the output of basis weight gauge 31 while the gauge is making a newscan, which occurs 20 minutes subsequent to the scan which resulted inthe previously stored profile average signal. To derive the averagesheet basis weight signal while gauge 31 is in the scanning mode, theoutput of profile average computer 103 is applied to analog memory 108through switch 109 at the same time that the output of subtracter 104 isapplied to analog memory 106. Memory 108 stores the profile averageoutput of computer 103 until the contacts of normally open switch 109are again closed by the output of programmer 41. The output of analogmemory 108 is coupled through switch 11 1 to the subtrahend input ofsubtraction circuit 112 during the entire time while gauge 31 isscanning across the sheet in response to a control signal applied to theswitch by programmer 41. During the interval while gauge 31 is scanningacross the width of the sheet, programmer 41 activates switch 107 sothat the output voltage of memory 106 is decoupled from the subtrahendinput of difference circuit 101. Thereby, the minuend inputto-differencenetwork 112 is responsive solely to the output voltage of basis weightgauge 31 and the output voltage of network 112 is a DC analog voltageproportional to the instantaneous basis weight of gauge 31 while it isin the scanning mode minus the profile average basis weight taken forthe previous scan of gauge 31.

While basis weight gauge 31 is in the single point mode the subtrahendinput-to-subtraction network 112 is zero because switch 111 ismaintained in an open circuit condition in response to the output ofprogrammer 41. Hence, the average basis weight difference signal derivedfrom subtraction network 101 is coupled directly through differencenetwork 112.

It is to be recognized that the circuit of FIG. 3 can also be employed,with slight modification, for each of measuring circuits 43 and 44. Itis to be recalled that dry end gauges 32 and 33 scan across the width ofthe sheet continuously, except for a l-minute time interval while theyare in the single point mode. Gauges 32 and 33 are positioned, while inthe single point mode, at the same location across the sheet width aswet end gauge 31 while it is in the single point mode. Dry end gauges 32and 33 are in the single point mode during the first minute while wetend gauge 31 is being scanned, whereby identical cross and in machinesections of the sheet are detected by all of gauges 31-33. To enable acomparison of the data derived from gauges 32 and 33 while they are inthe single point mode to be made with the corresponding data derivedfrom the sheet while gauge 31 is in the last minute of single pointoperation prior to scanning, each of measuring circuits 43 and 44subtracts from the instantaneous output of the gauge to which it isresponsive the deviation of the single point measurement from theprofile average derived from the previous scan of the gauges.

To these ends, FIG. 3 is modified so that networks 101-103 areresponsive to the output signals of detectors 32 or 33, depending uponwhether circuit 43 or 44 is being considered. For purposes of simplicityin explanation, basis weight gauge 31 of FIG. 3 is assumed to bereplaced with basis weight gauge 32 in considering the manner by whichmeasuring circuit 43 functions. It is to be understood that measuringcircuit 44 responds to moisture gauge 33 in exactly the same manner asto be described for measuring circuit 43.

While the basis weight gauge at the dry end is scanning,profile-averaging computer 103 is activated by programmer 41; at thesame time programmer 41 open circuits each of switches 105, 107, 109 and111. Thereby, the output signal of subtraction network 112 is a measureof the instantaneous basis weight sensed by scanning gauge 32, whichsignal is coupled to basis weight fraction-defective computer 63, aswell as to composite fiber profile controller 81, the latter connectionbeing via multiplier 79. Upon the completion of each scan of basisweight gauge 32, the output voltage of profile average computer 103 is ameasure of the average basis weight across the sheet width. The signalaccumulated by computer 103 during each scan is normally read from theaverage computer upon the completion of each scan in response to asignal from programmer 41, which simultaneously discharges capacitors inthe averaging network to zero. The output of averaging computer 103,however, is normally decoupled from any of the other circuits in thenetwork since all of switches 105, 107, 109 and 111 are open-circuitedby a control signal from programmer 41.

Upon completion of the scan immediately preceding operation of gauge 32in the single point mode, programmer 41 derives a control signal toclose switches 105 and 107. A microswitch is provided to enablesampIe-and-hold network 102 in response to each passage of gauge 32 overthe single point location. Upon the completion of each scan of gauge 32there is thereby derived from subtracter 104 a voltage proportional tothe difference in the average and single point basis weights. Thesubtracter 104 DC analog output voltage is coupled to memory 106 only inresponse to switch 105 being closed by programmer 41 once every minutes,immediately prior to gauge 32 being driven to the single point mode.With the closure of switch contacts 105 analog memory 106 is therebyreloaded once every 20 minutes with a signal indicative of the departurein dry end basis weight at the single point location from the averagebasis weight across the sheet.

The output of memory 106 is coupled to the subtrahend input ofsubtraction circuit 101 during the entire l-minute interval while gauge32 is in the single point mode in response to the contacts of switch 107being closed during said time by programmer 41. Thereby, the outputvoltage of subtracter 101 is indicative of profile average basis weightof the sheet for each instant during a l-minute interval while gauge 32is in the single point mode. The output of subtracter 101 is fed throughsubtracter 112 in unmodified form since the subtracter subtrahend inputsignal is zero and coupled through switch 51 as indicated supra toenable the adaptive constant k to be recomputed once every 20 minutes.

Reference is now made to FIG. 4 of the drawings wherein is illustrated aschematic diagram of an analog computer version of thefraction-defective computer. The fraction-defective computer of FIG. 4may be utilized, with slight modification, either as computer 61 or 63to determine the fraction defective of dry end moisture or fibercontent, respectively. It is to be recalled from the discussion of FIG.2 and equation 4 that fraction defective is the ratio of the amount oftime the monitored variable is less than or greater than a limit amountof the variable compared to the total time paper is being manufactured,a ratio of two areas or integrals.

From equation 4, the integral comprising the numerator of the ratio isthe total-time the amount of material is greater or less than a limit;determined with the circuit of FIG. 4 by upper channel 121. Channel 121includes diode 122 connected in series between input terminals 120, DCvoltage source 123 and relay winding 127 which is energized whenever thenormally back-biased path through the diode and DC source is renderedinto a low impedance state. Energization of relay 127 results innormally open-circuited contact 128 being closed to couple a referencevoltage from source 129 to the input of DC analog integrator 124, whichis reset by programmer 41 once every 20 minutes. The potential M of DCsource 123 is variably controlled by the paper maker to correspond withthe acceptable limit or boundary of moisture or basis weight, asindicated by the reject limit line of FIG. 2.

DC source 123, in combination with diode 123, establishes the rejectlimit because the combination respectively represents open and shortcircuit conditions for voltages at terminals 120 greater and less than MIn response to the circuit comprising diode 122 and source 123 beingrespectively activated to the short and open circuit conditions, thereference voltage of source 129 is fed directly to integrator 124 or theintegrator 124 input is zero. Integrator responds to the zero orpredetermined finite voltage fed thereto to derive an output having anamplitude of the dividend of equation 4, supra.

The output voltage of integrator 124 is compared with a signalindicative of the total time upper channel 121 has been activated sincethe last reset of integrator 124, i.e., the activa tion time of theprocess or defective computer. The activation time signal is derived byfeeding a constant DC voltage from source 130 to the input terminals ofintegrator 125, which is reset simultaneously with integrator 124.Thereby, the output of integrator 125 is a sawtooth voltage increasingin amplitude linearly as a function of time relative to the last resetof integrators 124 and 125. Comparison of the outputs of integrators 124and 125 is performed in analog division network 126. Division network126 includes dividend and divisor inputs respectively responsive to theDC output voltages of integrators 124 and 125. Thereby, the outputvoltage of division network 126 is a DC signal having an amplitude equalto the ratio of the amount of defective product, i.e., the amount ofproduct having a value outside the limit M to the total amount of theproduct. As indicated supra, the ratio output of division network 126is, therefore, indicative of the percentage of the sheet havingdefective moisture or basis weight, referred to herein as fractiondefective.

Reference is now made to FIG. 5 of the drawings wherein there isillustrated a schematic diagram of the apparatus comprising fiber flowcontroller 84. Broadly, it is the function of controller 84 to adjustvalves 35 and 36 so that a fiber flow set point derived from integrator282 is attained for the slurry fed to pump 14 and headbox 15.

Controller 84 responds to a fiber flow rate set point signal derived byfeeding the output of integrator 282 and to consistency and flow ratetransducers 85 and 88 in line 13 respectively upstream and downstream ofvalve 36 to derive a signal indicative of the amount of fiber flowchange that should be made. The fiber flow change signal is combinedwith the actual flow signal derived from transducer 88 to establish asignal indicative of corrected fiber flow into pump 14. If the correctedfiber flow exceeds a limit established by the properties of valve 36 onthe total mass fiber mixture, valve 35 for the clear water source 11 isactivated. Otherwise, valve 35 is maintained at a preselected point andthe consistency of the mixture flowing in pipe 13 is not changed.

To these ends, the circuit of FIG. 5 includes multiplier 141 responsiveto the consistency and flow rate output signals of transducers 85 and88, respectively. The output signal of multiplier 141 is, therefore, aDC amplitude proportional to the actual fiber flow into pump 14 frompipe 13. The fiber flow output signal of multiplier 141 is compared insubtraction circuit 142 with the set point fiber flow derived fromintegrator 282. The output of difference circuit 142, indicative of thefiber flow error, is applied as a numerator input to division circuit143, the dividend input of which is the DC output of consistencytransducer 85.

In response to the inputs applied thereto, division circuit 143 derivesa signal proportional in amplitude to the error or change to be effectedbetween the actual flow and the desired flow, as reflected by the flowrate output of subtraction circuit 142. The change in the flow rate ofthe mixture in pipe 13 is combined with the actual flow rate derivedfrom transducer 88 in analog computer summing network 144, the resultantoutput of which is applied to limit detector 145.

Limit detector derives a binary 1 signal only in response to the outputof adding circuit 144 exceeding or being equal to a predetermined limit,commensurate with the limit of flow which can be passed through valve36. Whenever the output of adding circuit 144 indicates that the flowwould be less than the limit that valve 36 is capable of passing, theoutput of limit detector 145 is a binary 0.

The binary output signal of limit detector 145 is applied as a controlvoltage to switch 146, whereby the switch armature 147 respectivelyengages contacts 148 and 149 in response to the binary O and l outputsof limit detector 145. Switch 146 selectively gates the output voltageof adding circuit 144 to the servoloops for valves 35 and 36. Witharmature 147 engaging contact 148, the output voltage of adding circuit144 is applied directly to one of the inputs of subtraction network 89in the feedback loop controlling valve 36. In contrast, engagement ofarmature 147 and contact 149 results in the output voltage of addingcircuit 144 being applied to an input of subtraction network 86 in theservoloop for control of valve 35.

The signal applied to the servoloop controlling valve 36 can be applieddirectly, without modification, since the signal for controlling valve35 must be altered to reflect a predetermined consistency control. Tothis end, terminal 149 is connected to the numerator input of divisioncircuit 151, the divisor input of which is responsive to theflow-indicating output of transducer 88. In response to a finite fiberflow change numerator signal being applied thereto through switch 147,devisor signal 151 derives an output voltage indicative of one plus theratio of the flow rate change calculated by division circuit 143 to theactual flow rate in pipe 13, as derived from transducer 88. Theconsistency output signal of division circuit 151 is combined in adder152 with a predetermined DC voltage from source 153 and indicative ofthe predetermined consistency for the ratio of fiber to clear water fromsources 12 and 11, respectively. The output of adder 152 is applied toan input of subtraction network 86 in the feedback loop controllingvalve 35. Thereby, if the limit established by detector 145 is notexceeded by the output of adder 144, the preset input to summing network152 is constantly applied to the servoloop for valve 35. In the eventthe limit of detector 145 is exceeded, however, valve 36 is driven toits widest opening and valve 35 is controlled in response to theerror-indicating consistency signal derived from division circuit 151,as well as from the preset signal applied to adder 152.

Because the fiber set point input signal to controller 84 is derivedprimarily from wet end gauge 31, the dry end fraction defective signalbeing of very low frequency and not subject to short term variations,the fiber controller output signals can be applied continuously orapproximately once every 15 seconds to the actuators of valves 35 and36. In contrast, prior art techniques relying upon gauge readings at thedry end of the process limit the application of control signals to thevalve actuators to a periodicity of the total process transport lag, 1.5minutes generally. Continuous or l5-second control can be effected withthe present invention because it is not necessary to wait a protractedtime interval prior to determining what effect the control action has onthe product.

Reference is now made to FIG. 6 of the drawings wherein there isdisclosed in block diagram form the apparatus comprising moisturecomputer 66. It is to be recalled that the function of moisture computer66. It is to determine the drying rate of steam dryer 21 and trim dryer25. In general, the moisture computer responds to the wet endmoisture-indicating output signal of multiplier 58 and immediatelyapplies a control signal to slow response time steam dryer 21.Simultaneously, the wet end moisture-indicating output signal is delayedfor a time commensurate with the transport lag between wet end gauge 31and trim dryer 25 and is combined with the moisture fraction-defectiveerror output of integrator 262 to derive a signal indicative of thetotal drying rate requirement of both the steam and trim dryers insection 19. The total drying rate requirement signal is compared witherror signals from the steam and trim dryers to control the trim dryerdrying rate.

Referring to FIG. 6 in particular, the wet end moisture output ofmultiplier 58 is fed through delay element 161, having a delay time ofapproximately 1 minute, the transport lag between wet end gauge 31 andtrim dryer 25, to computer 162 which derives an output signal indicativeof the total drying rate requirement of dryer section 19. Computer 162scales the delayed wet end moisture signal by a constant R and linearlycombines the resultant with the output of integrator 262. Thereby, theDC output voltage, (V,-,,,,) of computer 162 indicative of the set pointfor the drying rate of dryer 19 is represented as:

inat 1( W)D+fEFDMdt where:

R,=constant,

(M wet end moisture delayed for the transport lag between gauge 31 andtrim dryer 25, and

EFDM=fraction-defective error in moisture.

The total drying rate requirement indicating output signal of computer162 is compared in analog summing circuit 163 with the actual dryingrate of steam dryer 21 and the actual drying rate of trim dryer 25.Analog summing circuit 163 responds to the stated inputs thereof toderive a trim dryer set point voltage in accordance with:

F m lmrl where:

VF-the set point for trim dryer 25,

V =the actual drying rate of steam dryer 21, and

V,,, ,,=the total drying rate requirementof both the steam and trimdryers, as derived by the output of computer 162.

Prior to considering the manner by which the signal V, is derived,consideration will be given to the control apparatus for steam dryers21. Steam dryers 21 are responsive to the wet end moisture indications,M derived from multiplier 58 immediately upon the derivation thereof.The wet end moisture indicating output of multiplier 58 is scaled by apredetermined constant, R in analog multiplication network 164, theoutput of which is a DC signal indicative of the required drying rate ofdryer section 19. V is also used to represent the set point drying ratefor steam rollers 21. Because of the inherent lag of steam dryers 21,the set point output voltage of multiplier 164 is applied directly tothe input of a servosystem including analog difference network 67, theoutput of which drives integral controller 72 for valve 23 in the steamline.

Difference network 67 is also responsive to a DC signal indicative ofthe actual drying rate of steam dryers 21. A signal representing actualdrying rate of dryers 21 is derived from measurements of the actualaverage temperature in steam dryers 21, generated by temperaturetransducers 68 and 69, having outputs which are fed to computer 71.Computer 71 comprises a nonlinear function generator of a known typewhich isemperically calibrated to relate the surface temperatures of thedryer to the drying rates determined from experimental data. It respondsto the average of DC voltages generated by the transducers as at 68 and69 to derive a voltage that is fed to difference 67 and is proportionalto the actual drying rate of steam dryers 21.

The set point for driving all of the sections comprising trim dryer 25is adjusted to enable the trim dryer to remove any moisture from thesheet that should have been, but was not, removed by steam dryer 21. Theset point signal is thereby derived by subtracting in analog differencecircuit 613 the total drying rate requirement DC output signal ofcomputer 162 from the output signal of computer 71, indicative of theactual drying rate for steam dryers 21. The DC output of differencenetwork 163 is compared in analog subtraction circuit with the actualtrim dryer drying rate signal generated by temperature transducer 65mounted in the fast-response time dryer. Difference circuit 165 derivesan error signal for controlling all of sections of the trim dryer 25alike, which error signal is coupled to dryer controllers 73 via adders77, as indicated supra.

To provide a better understanding of the drying system operation, let itbe initially assumed that the same wet end moisture and moisturefraction-defective error signals have been derived from multiplier 52and subtractor 63 for a relatively long time period. Under suchcircumstances, the conditions of steam dryer 21 and trim dryer 25 arestabilized and zero error signals are applied to controllers 72 and 77.Now let it be assumed that a moist spot in the sheet is detected by wetend basis weight gauge 31, as reflected in the output signal ofmultiplier 58. At the same time, it is assumed that the slowly varyingmoisture fraction-defective error remains constant.

Under the assumed conditions, the wet end moisture output signal ofmultiplier 58 is sealed in multiplier 164 and applied to error-sensingsubtraction circuit 67. Subtraction circuit 67 thereby derives an errorsignal indicative of the amount by which the steam applied by source 22to dryers 21 should be increased. The error signal generated by circuit67 is applied to controller 72 that drives valve 23 to be open to agreater extent and additional steam is coupled from source 22 to dryers21. The dryers, however, do not respond instantly to steam from source22, but have an exponential rise in drying capabilities with a timeconstant on the order of 2 minutes. While the drying rate of steamdryers 21 slowly increases, the output of computer 71 also increases andthe error output of difference circuit 67 is decreased slightly.

During the first minute after the wet spot had been detected by gauge31, the increase in the drying rate occasioned by steam dryers 21 iscompensated with a decrease in the drying rate of trim dryer 25 throughcontrol of trim dryer 25 servoloop by circuit 163. The trim dryer dryingrate is decreased because of the transport lag between wet end gauge 31and trim dryer 25 and occurs because the output voltage of computer 163is decreased in response to the increasing value of the value of V,while the value of V,,,,,,, the output of computer 162, remainsconstant.

Upon completion of the l-minute transport lag between wet end gauge 31and trim dryers 25, the wet end moisture change is reflected in theoutput of delay element 161 and is fed to computer 162. The computerresponds immediately to the change in wet end moisture set point inputfed thereto to derive a signal indicating that the total drying raterequirement of section 19 has increased, reflecting the presence of theentire moisture region of the sheet now being in the dryer. When theoutput of computer 162 suddenly increases, the actual drying rate ofsteam dryers 21 has increased to approximately 40 percent of the changederived 1 minute earlier from the output of multiplier 58. The outputvoltage of computer 163 responds to the difference in the V, and Voutputs of computers 71 and 162 to derive an indication that the other60 percent of the desired drying rate of dryer 19 must be made up bytrim dryer 25. The change in the set point of trim dryer 25 at this timeis, however, equal to the change in the output of computer 163 since thetrim dryer output was previously reduced to compensate for the slow risein the actual drying rate of steam dryers 21. As time progresses, themoisture actually removed by steam dryers 21 increases to a pointwhereby the error-indicating output signal of difference network 67 isagain zero. Under such circumstances, it is no longer necessary tocompensate for the lag of the steam dryers and the output of computer163 is returned to the same value as was derived therefrom prior to thechange in the sheet condition discussed.

While there has been described and illustrated one specific embodimentof the invention, it will be clear that variations in the details of theembodiment specifically illustrated and described may be made withoutdeparting from the true spirit and scope of the invention as defined inthe appended claims. For example, the analog computer apparatusdisclosed herein can be replaced with a digital computer system havingeither a hard wire or software program to control the sheet manufacture.In addition, activation of the various controllers may be effectedmanually in response to visual indications of the various controlsignals derived, instead of automatically.

We claim:

31. In a process control system responsive to property measurement of amaterial, means responsive to the measurement for deriving a firstsignal indicative of the actual fraction of the material having aproperty value outside of a reject limit, means comparing said firstsignal with a value indicative of a set point for the fraction forderiving an error signal, and means responsive to the error signal forcontrolling the magnitude of a target value for the property in such amanner tha the target value for the property is varied to approach thelimit is response to the actual fraction being less than the fractionset point and to recede from the limit in response to the actualfraction being greater than the fraction set point.

2; The system of claim 1 wherein said first signal-deriving meansincludes means responsive to the measurement for computing:

where:

x =the instantaneous value of the property,

T=the length of the integrating interval, t,=the instant of time atwhich the integrating interval T begins, !=time, x the reject limit,f(xx,,,= x less than x f(xx,,,=, x equal to or greater than x 3.Apparatus for deriving a signal indicating the value of a set pointsignal for controlling the drying rate of dryers in apaper-manufacturing system fabricating a sheet, comprising gauge meansresponsive to the quantity of moisture in the sheet for deriving a firstsignal proportional to the moisture quantity, means responsive to thefirst signal for computing an indication of moisture fraction defectivein response to a comparison of moisture content relative to anindication of a preset moisture content reject limit, means forcombining the computed moisture fraction defective with a set point formoisture fraction defective of the paper to derive an error signalhaving one polarity when the computed moisture fraction defectiveexceeds the set point and the opposite polarity when the computedmoisture fraction defective is less than the set point, and means forcontrolling the magnitude of a set point signal of an actuatorcontrolling sheet moisture in response to the error signal in adirection tending to reduce the error signal to zero regardless of theerror signal polarity.

4. The apparatus of claim 3 including gauge means for deriving anothersignal indicative of dryer drying rate, and means responsive to saidanother signal and the actuator set point signal for controlling thedrying rate of the dryer.

5. The apparatus of claim 3 including gauge means for deriving anothersignal indicative of dryer drying rate, means responsive to said anothersignal and the actuator set point signal for controlling the drying rateof the dryer, another gauge means for detecting the fiber content of thesheet, means responsive to the another gauge for deriving a secondsignal proportional to fiber content fraction defective, means forcombining the second signal with a set point for fiber fractiondefective of the paper to derive a second error signal, means forcontrolling the magnitude of a fiber set point signal in response to thesecond error signal, and means responsive to the second error signal forcontrolling the fiber flowing into the process.

6. Apparatus for deriving a signal indicating the value of a set pointsignal for controlling the flow of fibers into a papermanufacturingsystem comprising gauge means responsive to the quantity of fiber in thesheet for deriving a first signal proportional to the fiber quantity,means responsive to the first signal for computing a first indication ofa fiber content fraction defective from a comparison of fiber contentrelative to an indication of a preset fiber content reject limit,further including means for combining the computed fiber fractiondefective with a set point for fiber fraction defective of the paper toderive an error signal having one polarity when the computed fiberfraction defective exceeds the set point and the opposite polarity whenthe computed fiber fraction defective is less than the set point, andmeans for controlling the magnitude of a set point signal of an actuatorcontrolling sheet fiber content in response to the error signal in adirection tending to reduce the error signal to zero regardless of theerror signal polarity.

7. The apparatus of claim 6 including gauge means for deriving anothersignal indicative of actual fiber flow rate, means responsive to saidanother signal and the set point signal for controlling the fiberflowing into the process.

8. The apparatus of claim 6 further including gauge means responsive tothe quantity of moisture in the processed sheet for deriving a secondsignal proportional to the moisture quantity, means responsive to thesecond signal for deriving an indication of a statistical function ofthe paper quality from a comparison of moisture content relative to anindication of a preset moisture content reject limit, means forcontrolling the paper fiber in response to a comparison of said firstindication with the set point therefore, and means for controlling themoisture content in 9. A method of controlling a process treating amaterial comprising the steps of indicating the fraction of the materialhaving a property value outside of a reject limit, comparing saidfraction with a preselected value of the fraction, and controlling aparameter of the process in response to said comparison so that thecompared fractions are substantially equalized regardless of thedirection in which said indicated fraction deviates from saidpreselected value thereof.

10. A system for controlling a property of a material being formed by amanufacturing process or machine comprising gauge means monitoring theproperty for deriving a first signal indicative of the propertyvariations, means responsive to the first signal and an indication of avalue for the property commensurate with a property reject limit forderiving a second signal indicative of the fraction of the materialhaving a property value outside of the reject limit, means comparing thesecond signal with an indication of a set point for the fraction of thematerial outside of the reject limit for deriving an error signal havingone polarity when the fraction exceeds the set point and the oppositepolarity when the fraction is less than the set point, an actuator forcontrolling the property, a set point source for the actuator, meansresponsive to the set point source for controlling the actuator inresponse to the actuator set point magnitude, and means responsive tothe error signal for controlling the magnitude of the actuator set pointin such a manner that the actuator controls the property in a mannertending to reduce the error signal to zero magnitude regardless of theerror signal polarity.

ll. The system of claim wherein the actuator control means includesmeans comparing a signal derived from the gauge means and the actuatorset point for deriving another error signal, and means for coupling theanother error signal to the actuator.

12. In a method for controlling the average value of a property of amaterial in response to a measurement of the property, calculating in aresponse to a measurement of the property, calculating in a computermeans the fraction of the material having a property value outside of areject limit, in the computer means comparing the calculated fractionwith a set point for the fraction to derive an indication of the errorbetween the set point and calculated values of the fraction,

and in response to the error indication controlling the mag nitude of aset point value for the property in such a manner that the set pointvalue is varied to approach and to recede from the limit in response tothe calculated fraction being less than and greater than the fractionset point, respectively.

13. The method of claim 12 further including the step of controlling anactuator affecting the property in response to the set point value.

14. A method for controlling a property of a material being formed by amanufacturing process or machine comprising the steps of monitoringvariations of the material property, in response to the monitoredproperty variations and an indication of a value for the propertycommensurate with the property reject limit deriving an indication ofthe fraction of the material having a property value outside of thereject limit,

comparing the indication of the fraction of the material having aactuator set point is changed in a manner tendin to reduce the errorsignal to zero magnitude regardless o the error signal polarity.

15. The method of claim 14 further including the step of comparing anindication of the condition of the actuator and the actuator set pointfor deriving another error indication, and in response to the anotherindication setting the actuator.

16. A method for controlling a property of a material being formed by amanufacturing process or machine comprising the steps of monitoring theproperty to derive a first signal indicative of the property variations,in a computer means responsive to the first signal and an indication ofa value for the property commensurate with a reject limit deriving asecond signal indicative of the fraction of the material having aproperty value outside of the reject limit, in the computer meanscomparing the second signal with an indication of a set point for thefraction of the material outside of the reject limit to derive an errorsignal having one polarity when the fraction exceeds the set point andthe opposite polarity when the frac tion is less than the set point, inthe computer means responding to the error signal to control themagnitude of the set point for an actuator controlling the property,said actuator set point being controlled so that the actuator set pointis changed in a manner tending to reduce the error signal to zeromagnitude regardless of the error signal polarity, and controlling theactuator in response to the actuator set point indication.

2. The system of claim 1 wherein said first signal-deriving meansincludes means responsive to the measurement for computing: where: x theinstantaneous value of the property, T the length of the integratinginterval, tithe instant of time at which the integrating interval Tbegins, t time, xR the reject limit, f(x-xR) 0 for x less than xR f(x-xR) 1 for x equal to or greater than xR
 3. Apparatus for deriving asignal indicating the value of a set point signal for controlling thedrying rate of dryers in a paper-manufacturing system fabricating asheet, comprising gauge means responsive to the quantity of moisture inthe sheet for deriving a first signal proportional to the moisturequantity, means responsive to the first signal for computing anindication of moisture fraction defective in response to a comparison ofmoisture content relative to an indication of a preset moisture contentreject limit, means for combining the computed moisture fractiondefective with a set point for moisture fraction defective of the paperto derive an error signal having one polarity when the computed moisturefraction defective exceeds the set point and the opposite polarity whenthe computed moisture fraction defective is less than the set point, andmeans for controlling the magnitude of a set point signal of an actuatorcontrolling sheet moisture in response to the error signal in adirection tending to reduce the error signal to zero regardless of theerror signal polarity.
 4. The apparatus of claim 3 including gauge meansfor deriving another signal indicative of dryer drying rate, and meansresponsive to said another signal and the actuator set point signal forcontrolling the drying rate of the dryer.
 5. The apparatus of claim 3including gauge means for deriving another signal indicative of dryerdrying rate, means responsive to said another signal and the actuatorset point signal for controlling the drying rate of the dryer, anothergauge means for detecting the fiber content of the sheet, meansresponsive to the another gauge for deriving a second signalproportional to fiber content fraction defective, means for combiningthe second signal with a set point for fiber fraction defective of thepaper to derive a second error signal, means for controlling themagnitude of a fiber set point signal in response to the second errorsignal, and means responsive to the second error signal for controllingthe fiber flowing into the process.
 6. Apparatus for deriving a signalindicating the value of a set point signal for controlling the flow offibers into a paper-manufacturing system comprising gauge meansresponsive to the quantity of fiber in the sheet for deriving a firstsignal proportional to the fiber quantity, means responsive to the firstsignal for computing a first indication of a fiber content fractiondefective from a comparison of fiber content relative to an indicationof a preset fiber content reject limit, further including means forcombining the computed fiber fraction defective with a set point forfiber fraction defective of the paper to derive an error signal havingone polarity when the computed fiber fraction defective exceeds the setpoint and the opposite polarity when the computed fiber fractiondefective is less than the set point, and means for controlling themagnitude of a set point signal of an actuator controlling sheet fibercontent in response to the error signal in a direction tending to reducethe error signal to zero regardless of the error signal polarity.
 7. Theapparatus of claim 6 including gauge means for deriving another signalindicative of actual fiber flow rate, means responsive to said anothersignal and the set point signal for controlling the fiber flowing intothe process.
 8. The apparatus of claim 6 further including gauge meansresponsive to the quantity of moisture in the processed sheet forderiving a second signal proportional to the moisture quantity, meansresponsive to the second signal for deriving an indication of astatistical function of the paper quality from a comparison of moisturecontent relative to an indication of a preset moisture content rejectlimit, means for controlling the paper fiber in response to a comparisonof said first indication with the set point therefor, and means forcontrolling the moisture content in
 9. A method of controlling a pRocesstreating a material comprising the steps of indicating the fraction ofthe material having a property value outside of a reject limit,comparing said fraction with a preselected value of the fraction, andcontrolling a parameter of the process in response to said comparison sothat the compared fractions are substantially equalized regardless ofthe direction in which said indicated fraction deviates from saidpreselected value thereof.
 10. A system for controlling a property of amaterial being formed by a manufacturing process or machine comprisinggauge means monitoring the property for deriving a first signalindicative of the property variations, means responsive to the firstsignal and an indication of a value for the property commensurate with aproperty reject limit for deriving a second signal indicative of thefraction of the material having a property value outside of the rejectlimit, means comparing the second signal with an indication of a setpoint for the fraction of the material outside of the reject limit forderiving an error signal having one polarity when the fraction exceedsthe set point and the opposite polarity when the fraction is less thanthe set point, an actuator for controlling the property, a set pointsource for the actuator, means responsive to the set point source forcontrolling the actuator in response to the actuator set pointmagnitude, and means responsive to the error signal for controlling themagnitude of the actuator set point in such a manner that the actuatorcontrols the property in a manner tending to reduce the error signal tozero magnitude regardless of the error signal polarity.
 11. The systemof claim 10 wherein the actuator control means includes means comparinga signal derived from the gauge means and the actuator set point forderiving another error signal, and means for coupling the another errorsignal to the actuator.
 12. In a method for controlling the averagevalue of a property of a material in response to a measurement of theproperty, calculating in a computer means the fraction of the materialhaving a property value outside of a reject limit, in the computer meanscomparing the calculated fraction with a set point for the fraction toderive an indication of the error between the set point and calculatedvalues of the fraction, and in response to the error indicationcontrolling the magnitude of a set point value for the property in sucha manner that the set point value is varied to approach and to recedefrom the limit in response to the calculated fraction being less thanand greater than the fraction set point, respectively.
 13. The method ofclaim 12 further including the step of controlling an actuator affectingthe property in response to the set point value.
 14. A method forcontrolling a property of a material being formed by a manufacturingprocess or machine comprising the steps of monitoring variations of thematerial property, in response to the monitored property variations andan indication of a value for the property commensurate with the propertyreject limit deriving an indication of the fraction of the materialhaving a property value outside of the reject limit, comparing theindication of the fraction of the material having a property valueoutside the reject limit with an indication of a set point for thefraction of the material outside of the reject limit to derive an errorsignal having one polarity when the fraction exceeds the set point andthe opposite polarity when the fraction is less than the set point, inresponse to the error signal controlling the set point for an actuatorcontrolling the property, said actuator set point being controlled sothat the actuator set point is changed in a manner tending to reduce theerror signal to zero magnitude regardless of the error signal polarity.15. The method of claim 14 further including the step of comparing anindication of the condition of the actuator and the actuator set pointfor deriving another error indication, and iN response to the anotherindication setting the actuator.
 16. A method for controlling a propertyof a material being formed by a manufacturing process or machinecomprising the steps of monitoring the property to derive a first signalindicative of the property variations, in a computer means responsive tothe first signal and an indication of a value for the propertycommensurate with a reject limit deriving a second signal indicative ofthe fraction of the material having a property value outside of thereject limit, in the computer means comparing the second signal with anindication of a set point for the fraction of the material outside ofthe reject limit to derive an error signal having one polarity when thefraction exceeds the set point and the opposite polarity when thefraction is less than the set point, in the computer means responding tothe error signal to control the magnitude of the set point for anactuator controlling the property, said actuator set point beingcontrolled so that the actuator set point is changed in a manner tendingto reduce the error signal to zero magnitude regardless of the errorsignal polarity, and controlling the actuator in response to theactuator set point indication.